Collective quantification and the homogeneity constraint

Abstract

<p>The main theoretical claim of the paper is that a slightly revised version of the analysis of mass quantifiers proposed in Roeper 1983, Lønning 1987 and Higginbotham 1994 extends to <em>collective</em> quantifiers: such quantifiers denote <em>relations between sums of entities</em> (type e), <em>rather than relations between sets of sums</em> (type <e,t>). Against this background I will explain a puzzle observed by Dowty (1986) for <em>all</em> and generalized to all quantifiers by Winter 2002: plural quantification is not allowed with all the predicates that are traditionally classified as ”collective”. The Homogeneity Constraint – as well as the weaker requirement of divisiveness - will be shown to be too strong (for both collective and mass quantifiers). What is required is that the nominalization of the nuclear-scope predicate denotes a maximal sum (rather than a group). Divisiveness is a sufficient, but not a necessary condition for this to happen. Non-divisive predicates such as <em>form a circle</em>, which denote sets of ‘extensional’ groups are allowed, because extensional groups are equivalent to the maximal sum of their members. It is only intensional group predicates that block collective Qs.</p><p><strong>Keywords</strong>: collective quantification, mass quantification, homogeneous, cumulative, divisive, groups, sums, maximality operator, plural logic</p>